Subject: [mg69261] Re: using FindRoot to find multiple answers in a domain?

From: Paul Abbott <paul at physics.uwa.edu.au>

Date: Mon, 4 Sep 2006 02:41:25 -0400 (EDT)

Organization: The University of Western Australia

References: <ed0rn9$sm6$1@smc.vnet.net> <ed3rou$rv5$1@smc.vnet.net>

Sender: owner-wri-mathgroup at wolfram.com

In article <ed3rou$rv5$1 at smc.vnet.net>, "akil" <akomur at wanadoo.nl>
wrote:
> IntervalRoots package and RootSearch do not work for the kind of formulas I
> have.
Are you sure?
> For example in the domain [0,Pi/2] we want to solve (I only used FindRoot
> because this was the fastest):
>
> I put the package I test in on
> http://home.wanadoo.nl/akomur/testRootSearch.nb so that you can see the
> formulas I use.
>
> Copying them In here ruins the formulas.
Copy as Plain text. Your first formula is
nlv = Max[-81.24275115593154 Cot[beta] - 48.489352280270914,
Min[-46.844746272761526 Cot[beta] - 71.4213555357176,
-46.480384751324436 Cot[beta] - 71.66426321667566]]
Note that PiecewiseExpand can be applied to such formulae. If you
simplify the result
Simplify[PiecewiseExpand[nlv]]
you deduce that nlv is just
-81.24275115593154 Cot[beta] - 48.489352280270914 if Cot[beta] <= 2/3
-46.844746272761526 Cot[beta] - 71.4213555357176 if Cot[beta] >= 2/3
You can check that these values are consistent when Cot[beta] == 2/3.
Moreover, the catch-all condition
-46.480384751324436 Cot[beta] - 71.66426321667566
is redundant for real beta since it only applies when Cot[beta] == 2/3.
A brief examination of nuvb shows that it involves ratios of (powers of)
expressions similar to nlv. I expect that simplification of these
expressions prior to constructing nuvb would lead to a final form that
is not that hard to handle.
I expect that if you step back and tell us more about the original
problem, then a more elegant approach would present itself.
Cheers,
Paul
_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
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